Representation of musical rhythm and its classification system based on mathematical and geometrical analysis

One of the fundamental elements of music is rhythm and a rhythm is nothing but a combination of some claps and waves. Every pieces of music must follow some rhythms and music of different regions differs from each other. To identify the difference we have to retrieve the hidden rhythms of music and also have to identify its properties. A common way to represent a rhythm is as a binary format where dasia1psila indicates a clap (sound) and dasia0psila indicates a wave (silence). In this paper, mathematical and geometrical representation of rhythms is analyzed with a view to building a classification system that cans categories rhythms of various regions. Based on various distance matrices, Toussaint has shown a single polygonal model to classify Africa, Brazilian and Cuban rhythms. The same mechanism is followed and also applied on The North Indian rhythms, used in India and Bangladesh. In this paper, turning function, a function for polygon similarity measurement, is used to measure the distance among various rhythms. Various types of phylogenetic trees are also used to represent the graphical classification system. Single polygonal model to represent the rhythm is easier but there are some North Indian rhythms which are not possible to represent in that format. In this paper a multi polygonal model is proposed and shown its geometrical representation technique.